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Operating on Taylor Series

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Problems 1

Let S=∑n=1∞1n(n+1)⋅(n+1)!S = \sum_{n=1}^{\infty} \frac{1}{n(n+1)\cdot(n+1)!}S=∑n=1∞n(n+1)⋅(n+1)!1. Find the value of ln⁡(3−S)\ln(3 - S)ln(3−S). Source: HMMT February 2007